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Novel adaptive learning control of linear systems with completely unknown time delays

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Abstract

A novel output-feedback adaptive learning control approach is developed for a class of linear time-delay systems. Three kinds of uncertainties: time delays, number of time delays, and system parameters are all assumed to be completely unknown, which is different from the previous work. The design procedure includes two steps. First, according to the given periodic desired reference output and the allowed bound of tracking error, a suitable finite Fourier series expansion (FSE) is chosen as a practical reference output to be tracked. Second, by expressing the delayed practical reference output as a known time-varying vector multiplied by an unknown constant vector, we combine three kinds of uncertainties into an unknown constant vector and then estimate the vector by designing an adaptive law. By constructing a Lyapunov-Krasovskii functional, it is proved that the system output can asymptotically track the practical reference signal. An example is provided to illustrate the effectiveness of the control scheme developed in this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Xidian University, Xi’an, 710071, PRC

    Wei-Sheng Chen

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  1. Wei-Sheng Chen
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Correspondence to Wei-Sheng Chen.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60804021).

Wei-Sheng Chen received his B. Sc. degree in the Department of Mathematics from Qufu Normal University, Qufu, PRC, in 2000, the M. Sc. degree and Ph.D. degree in the Department of Applied Mathematics from Xidian University, Xi’an, PRC, in 2004 and 2007, respectively. In 2008, he was a visiting scholar in the Automation School at Southeast University, Nanjing, PRC, and is currently an associate professor in the Department of Applied Mathematics, Xidian University.

His research interests include adaptive control, learning control, neural network control, backstepping control for uncertain nonlinear systems such as time-delay or stochastic nonlinear systems.

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Chen, WS. Novel adaptive learning control of linear systems with completely unknown time delays. Int. J. Autom. Comput. 6, 177–185 (2009). https://doi.org/10.1007/s11633-009-0177-5

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  • DOI: https://doi.org/10.1007/s11633-009-0177-5

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